Strongly connected-HDU4635

Problem - 4635 http://acm.hdu.edu.cn/showproblem.php?pid=4635

题目大意：

n个点，m条边，求最多再加几条边，然后这个图不是强连通

分析：

这是一个单向图，如果强连通的话，他最多应该有n*(n-1)条边，假设有a个强连通块，任取其中一个强连通块,假设取出的这个强连通块里有x个点，剩下的（n-a）个点看成一个强连通块，如果让这两个强连通块之间不联通，肯定是这两个只有一个方向的边,最多就会有x*(n-x)条边  所以最多加n*(n-1)-x*x(n-x)-m边。所以当x最小是式子最大。

Problem Description

Give a simple directed graph with N nodes and M edges. Please tell me the maximum number of the edges you can add that the graph is still a simple directed graph. Also, after you add these edges, this graph must NOT be strongly connected.
A simple directed graph is a directed graph having no multiple edges or graph loops.
A strongly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in the direction(s) in which they point. 

 

Input

The first line of date is an integer T, which is the number of the text cases.
Then T cases follow, each case starts of two numbers N and M, 1<=N<=100000, 1<=M<=100000, representing the number of nodes and the number of edges, then M lines follow. Each line contains two integers x and y, means that there is a edge from x to y.

 

Output

For each case, you should output the maximum number of the edges you can add.
If the original graph is strongly connected, just output -1.

 

Sample Input

3
3 3
1 2
2 3
3 1
3 3
1 2
2 3
1 3
6 6
1 2
2 3
3 1
4 5
5 6
6 4

 

Sample Output

Case 1: -1
Case 2: 1
Case 3: 15

 

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<stack>
#include<queue>
#include<vector>

using namespace std;
#define N 100005
#define INF 0x3f3f3f3f

struct node
{
    int to,next;
}edge[N*];

int low[N],dfn[N],Time,top,ans,Stack[N],belong[N],sum,head[N],aa[N],in[N],out[N],Is[N];

void Inn()
{
    memset(low,,sizeof(low));
    memset(dfn,,sizeof(dfn));
    memset(Stack,,sizeof(Stack));
    memset(belong,,sizeof(belong));
    memset(head,-,sizeof(head));
    memset(aa,,sizeof(aa));
    memset(in,,sizeof(in));
    memset(out,,sizeof(out));
    memset(Is,,sizeof(Is));
    Time=top=ans=sum=;
}

void add(int from,int to)
{
    edge[ans].to=to;
    edge[ans].next=head[from];
    head[from]=ans++;
}

void Tarjin(int u,int f)
{
    low[u]=dfn[u]=++Time;
    Stack[top++]=u;
    Is[u]=;
    int v;
    for(int i=head[u];i!=-;i=edge[i].next)
    {
        v=edge[i].to;
        if(!dfn[v])
        {
            Tarjin(v,u);
            low[u]=min(low[u],low[v]);
        }
        else if(Is[v])
            low[u]=min(low[u],dfn[v]);
    }
    if(dfn[u]==low[u])
    {
        sum++;
        do
        {
            v=Stack[--top];
            belong[v]=sum;
            aa[sum]++;
            Is[v]=;
        }while(v!=u);
    }
}

void solve(int n,int m)
{
    for(int i=;i<=n;i++)
    {
        if(!dfn[i])
            Tarjin(i,);
    }
    if(sum==)
    {
        printf("-1\n");
        return ;
    }
    long long Max=;
    for(int i=;i<=n;i++)
    {
        for(int j=head[i];j!=-;j=edge[j].next)
        {
            int u=belong[i];
            int v=belong[edge[j].to];
            if(u!=v)
            {
                in[v]++;
                out[u]++;
            }
        }
    }
    long long c=n*(n-)-m;
    for(int i=;i<=sum;i++)
    {
        if(!in[i] || !out[i])
            Max=max(Max,c-(aa[i]*(n-aa[i])));
    }
    printf("%lld\n",Max);
}
int main()
{
    int T,n,m,a,b,i,t=;
    scanf("%d",&T);
    while(T--)
    {
        Inn();
        scanf("%d %d",&n,&m);
        for(i=;i<m;i++)
        {
            scanf("%d %d",&a,&b);
            add(a,b);
        }
        printf("Case %d: ",t++);
        solve(n,m);
    }
    return ;
}